5 problems

Let $G$ be a connected reductive group with Frobenius map $F$, and let $C$ be an $F$-stable unipotent class in $G$. For $u\in C^F$, write $A_G(u)$ for the component group associate…

Dudas–Malle conjecture. A similar order-reversing bijection result holds for twisted type $A$.

Dudas–Michel–He conjecture. The map $\Phi$ gives an order-reversing bijection

Lusztig's excellent-element conjecture. Then $u_w\in {\mathcal{O}}_C$.

Let $G$ be a simple adjoint algebraic group over $\mathbb{C}$, let $\mathcal{X}$ be the set of unipotent conjugacy classes in $G$, and let $\mathcal{W}$ be the Weyl group of $G$. F…